Hybrid particle swarm algorithm for solving nonlinear constraint optimization problems

Based on the combination of the particle swarm algorithm and multiplier penalty function method for the constraint conditions, this paper proposes an improved hybrid particle swarm optimization algorithm which is used to solve nonlinear constraint optimization problems. The algorithm converts nonlinear constraint function into no-constraints nonlinear problems by constructing the multiplier penalty function to use the multiplier penalty function values as the fitness of particles. Under the constraint conditions to make the particle swarm track the best particle and fly to the global best, this paper is to redefine p-best which is the particles position last iteration and g-best which refers to the best position of the group last iteration. And, by redefining p-best and g-best, the particle can avoid tracking the p-best and the g-best whose fitness are excellent but violate constraints to great extent, so that particle swarm would finally converge to the optimum position in the feasible domain. Numerical experiments show that the new algorithm is correct and effective. Key–Words: Particle swarm optimization; Multiplier method; Multiplier penalty function; Nonlinear constraint optimization; Nonlinear constraint; Global optimization.